Descriptions

A new method for evaluating the Lyapunov exponent for a Hamiltonian system
involves a spatial evaluation, rather than a numerical time integration. The
introduction of a novel vector field to the phase space allows the Lyapunov exponent
to be expressed in a form that does not involve time. The Lyapunov exponent
is seen to be a property of the geometry and topology of ergodic regions of phase
space. As a result it has a more regular behavior than previously thought. The
Lyapunov exponent is found to be a differentiable function of the perturbation coupling
in regions where it was previously thought to be discontinuous. Properties
of the Lyapunov function once taken for granted are shown to be artifacts of the
traditional computation methods. The technique is discussed with examples from a
system of coupled quartic oscillators.